Question

if sum of first 7 terms of an ap is 49 and that of 17 terms is 289 find sum of first n terms.....urgent plzz

Answer 1

S7 = 7 * (a1 + a7) / 2 = 49
7(a1 + a1 + 6d) / 2 = 49
2a1 + 6d = 14

S17 = 17 * (a1 + a17) / 2 = 289
17(a1 + a1 + 16d) / 2 = 289
a1 + 8d = 17

==> We have :
2a1 + 6d = 14
a1 + 8d = 17
a = 1, d = 2

an = 1 + (n - 1)*2
an = 2n - 1

Answer 2

let first term = a , common difference =d in an AP
1)sum 7 terms = s7 = 49
7/2[2a+6d] =49[here we used sn = n/2[2a+(n-1)d] formula]

7/2 *2 [a+3d] =49
7[a+3d] =49
a+3d =7----(1)
2)
sum of 17 terms =s17=289

17/2 [2a +16d]=289
17/2*2 [a+8d] =289
17[a+8d] =289
a+8d =17---(2)
subtract (1) from (2)
you get
5d =10

d= 10/5
d=2
substitute d=2 in (1)
a+3d=7
a+3*2=7
a+6=7
a=7-6
a=1
3)therfore a=1 and d=2

sn = n/2[2a+(n-1)d]
= n/2[2*1+(n-1)2]
=n/2[2+2n-2]
=n/2*2n
=n²